13.3 Relative conditional indirect effects

Before we use Hayes’s formulas at the top of pate 488 to re-express the posterior in terms of the relative conditional indirect effects, we might want to clarify which of the post columns correspond to the relevant parameters.

• \(a_{1}\) = b_respappr_D1
• \(a_{2}\) = b_respappr_D2
• \(a_{4}\) = b_respappr_D1:sexism
• \(a_{5}\) = b_respappr_D2:sexism
• \(b\) = b_liking_respappr

To get our posterior transformations, we’ll use the purrr::map() approach, which first requires we define two custom functions.

# (a1 + a4W)*b
D1_function <- function(w){
  (post$b_respappr_D1 + post$`b_respappr_D1:sexism`*w)*post$b_liking_respappr
  }

# (a2 + a5W)*b
D2_function <- function(w){
  (post$b_respappr_D2 + post$`b_respappr_D2:sexism`*w)*post$b_liking_respappr
  }

Next, we’ll make a 30-row tibble with each row containing a value for sexism, ranging from 3.5 to 6.5. We’ll then apply our two custom functions to the sexism values and wrangle the results a bit to make them useful for our purposes.

rcie_tibble <-
  tibble(sexism = seq(from = 3.5, to = 6.5, length.out = 30)) %>% 
  group_by(sexism) %>% 
  mutate(`Protest vs. No Protest`            = map(sexism, D1_function),
         `Collective vs. Individual Protest` = map(sexism, D2_function)) %>% 
  unnest() %>% 
  ungroup() %>% 
  mutate(iter = rep(1:4000, times = 30)) %>% 
  gather(`indirect effect`, value, -sexism, -iter) %>% 
  mutate(`indirect effect` = factor(`indirect effect`, levels = c("Protest vs. No Protest", "Collective vs. Individual Protest")))

head(rcie_tibble)

## # A tibble: 6 x 4
##   sexism  iter `indirect effect`         value
##    <dbl> <int> <fct>                     <dbl>
## 1    3.5     1 Protest vs. No Protest  0.160  
## 2    3.5     2 Protest vs. No Protest -0.0305 
## 3    3.5     3 Protest vs. No Protest -0.174  
## 4    3.5     4 Protest vs. No Protest -0.143  
## 5    3.5     5 Protest vs. No Protest -0.118  
## 6    3.5     6 Protest vs. No Protest  0.00955

Here is our variant of Figure 13.4, with respect to the relative conditional indirect effects.

rcie_tibble %>% 
  group_by(`indirect effect`, sexism) %>% 
  summarize(median = median(value),
            ll = quantile(value, probs = .025),
            ul = quantile(value, probs = .975)) %>% 
  
  ggplot(aes(x = sexism, group = `indirect effect`)) +
  geom_ribbon(aes(ymin = ll, ymax = ul),
              color = "white", fill = "transparent", linetype = 3) +
  geom_line(aes(y = median),
            color = "white") +
  coord_cartesian(xlim = 4:6,
                  ylim = c(-.6, .8)) +
  labs(x = expression(paste("Perceived Pervasiveness of Sex Discrimination in Society (", italic(W), ")")),
       y = "Relative Conditional Effect on Liking") +
  theme_black() +
  theme(panel.grid = element_blank(),
        legend.position = "none") +
  facet_grid(~ `indirect effect`)

Here are the indirect effect summaries relevant to the contents of Table 13.2.

rcie_tibble_pick_a_point <-
  # notice how we've restricted ourselves to only 3 values for `sexism`
  tibble(sexism = c(4.25, 5.125, 5.896)) %>% 
  group_by(sexism) %>% 
  mutate(`Protest vs. No Protest` = map(sexism, D1_function),
         `Collective vs. Individual Protest` = map(sexism, D2_function)) %>% 
  unnest() %>% 
  ungroup() %>% 
  # because we only have 3 `sexism` values, we only need to repeat `times = 3`
  mutate(iter = rep(1:4000, times = 3)) %>% 
  gather(`indirect effect`, value, -sexism, -iter) %>% 
  mutate(`indirect effect` = factor(`indirect effect`, levels = c("Protest vs. No Protest", "Collective vs. Individual Protest")))

rcie_tibble_pick_a_point %>% 
  group_by(sexism, `indirect effect`) %>% 
  summarize(median = median(value),
            ll = quantile(value, probs = .025),
            ul = quantile(value, probs = .975)) %>% 
  mutate_if(is.double, round, digits = 3)

## # A tibble: 6 x 5
## # Groups:   sexism [3]
##   sexism `indirect effect`                 median     ll    ul
##    <dbl> <fct>                              <dbl>  <dbl> <dbl>
## 1   4.25 Protest vs. No Protest             0.248  0.03  0.538
## 2   4.25 Collective vs. Individual Protest  0.225 -0.033 0.545
## 3   5.12 Protest vs. No Protest             0.518  0.288 0.807
## 4   5.12 Collective vs. Individual Protest  0.15  -0.021 0.347
## 5   5.90 Protest vs. No Protest             0.755  0.423 1.16 
## 6   5.90 Collective vs. Individual Protest  0.083 -0.152 0.331